PROPERTIES OF PHOSPHOR-BRONZE WIRES 



The ratios are given for each N after the number. The num- 

 ber of vibrations of the longest wire is arbitrarily taken as 

 unity in each case, and the ratios for the shorter -wires are fig- 

 ured on this basis. The mean of the four ratios for each length 

 are 1. 1.18, 2.03 and 2.13 with mean variations of 0. .01. .03 and 

 .07 respectively. 



The values for X.L are then 30. 27. 30.1 and 21.6. 



In the case of the wire in state III the lengths were 30. 22. 

 15 and 10 cms. The values for the above ratios of numbers of 

 vibrations in this case were 1. 1.72. 2.36 and 3.15. The values 

 for X.L are thus 30. 37.8, 35.1 and 31.5. We see that the pro- 

 duct X.L is roughly constant. It must be remembered that it 

 was impossible to make the periods exactly equal in the differ- 

 ent lengths, since the periods would have to be made equal at 

 equal amplitudes per unit length of the suspensions. This was 

 practically impossible. It is also evident that if the state of the 

 wire changes we could hardly expect a constant friction. This 

 point will be taken up again in the discussion of the loss of 

 energy in the two states. 



It should perhaps be said that the greater per cent of all the 

 cuiwes were either of type II or III and hence most of the data 

 are on these curves. State I seems to be more or less unstable 

 and is easily changed into state II. For these reasons type I 

 is omitted from the discussion. 



Variation of the initial amplitude. In a given sample of 

 wire, the number of vibrations required for the system to fall 

 through a given range of degrees, varies, in a general way. in- 

 versely with the mean amplitude of this range taken. In other 

 words the fall in amplitude is exponential. This is common to 

 all damped vibrations. 



In the phosphor-bronze wires the initial amplitude deter- 

 mines how rapid this fall shall be. If the initial amplitude is 



